Unformatted text preview: θ ? (d) Deduce that Z 35 ∼ = Z 5 × Z 7 . (3 points) 5. Let G be a group and let θ : S 3 → G be a homomorphism such that θ (( 1 2 )) = e G . (a) Prove that h ( 1 2 ) i ⊆ ker θ and h ( 1 2 ) i 6 S 3 . (b) Determine ker θ (why is ker θ 6 = h ( 1 2 ) i ?) (c) Deduce that θ (( 1 3 )) = e G . (3 points) (5 problems, 11 points altogether)...
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 Fall '08
 PARRY
 Algebra, Sets

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